# Consistency constraints for overlapping data clustering

@article{Culbertson2016ConsistencyCF, title={Consistency constraints for overlapping data clustering}, author={J. Culbertson and Dan P. Guralnik and J. Hansen and Peter F. Stiller}, journal={ArXiv}, year={2016}, volume={abs/1608.04331} }

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information… Expand

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